Rankin-Selberg methods for closed strings on orbifolds

Understand

In recent work we have developed a new unfolding method for computing one-loop modular integrals in string theory involving the Narain partition function and, possibly, a weak almost holomorphic elliptic genus.

• Unlike the traditional approach, the Narain lattice does not play any role in the unfolding procedure, T-duality is kept manifest at all steps, a choice of Weyl chamber is not required and the analytic structure of the amplitude is transparent.
• In the present paper, we generalise this procedure to the case of Abelian Z_N orbifolds, where the integrand decomposes into a sum of orbifold blocks that can be organised into orbits of the Hecke congruence subgroup {\Gamma}_0(N).
• As a result, the original modular integral reduces to an integral over the fundamental domain of {\Gamma}_0(N), which we then evaluate by extending our previous techniques.